An infinite surface with the lattice property I: Veech groups and coding geodesics

We study the symmetries and geodesics of an infinite translation surface which arises as a limit of translation surfaces built from regular polygons, studied by Veech. We find the affine symmetry group of this infinite translation surface, and we show that this surface admits a deformation into othe...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2014-05, Vol.366 (5), p.2625-2649
Main Author: HOOPER, W. PATRICK
Format: Article
Language:English
Subjects:
Automorphisms
Cylinders
Geodesy
Geometric planes
Homeomorphism
Mathematical lattices
Mathematical surfaces
Polygons
Triangulation
Vertices
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Summary:We study the symmetries and geodesics of an infinite translation surface which arises as a limit of translation surfaces built from regular polygons, studied by Veech. We find the affine symmetry group of this infinite translation surface, and we show that this surface admits a deformation into other surfaces with topologically equivalent affine symmetries. The geodesics on these new surfaces are combinatorially the same as the geodesics on the original.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-2013-06139-9